A rope is wound around a hollow cylinder of mass $$3$$ kg and radius $$40$$ cm. What is the angular acceleration of the cylinder, if the rope is pulled with a force of $$30$$ N? [NEET $$2017$$]

Question

Infinity Learn · Accepted Answer

Torque $$($$τ$$)$$  acting on a body and angular acceleration $$($$α$$)$$  produced in it are related asτ $$=$$ IαConsider a hollow cylinder around which a rope is wounded.Torque acting on the cylinder due to the force F is  τ$$=Fr$$.Now, we have  τ $$=$$ Iαwhere, I $$=$$ moment of inertia of the cylinder about the axis through the centre.⇒ $$I=mr2Given$$, $$F=30N$$,$$m=3kg$$ and $$r=40cm=40$$×$$10$$−$$2mAngular$$ acceleration,α$$=$$τ$$I=Frmr2=Fmr=303$$×$$40$$×$$10$$−$$2=1004=25rads$$−$$2$$

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder, if the rope is pulled with a force of 30 N? [NEET 2017]

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